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2 Graph the quadratic function y=-x+2x + 3. (the vertex and the intercepts)

2 Graph the quadratic function y=-x+2x + 3. (the vertex and the intercepts)

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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**Graphing Quadratic Functions** Graph the quadratic function \( y = -x^2 + 2x + 3 \). Analyze its key characteristics, including the vertex and the intercepts. ### Key Elements to Identify: 1. **Vertex:** - Use the vertex formula \( x = -\frac{b}{2a} \) to find the x-coordinate. - Calculate \( y \) by substituting \( x \) back into the equation. 2. **Intercepts:** - **y-intercept:** Set \( x = 0 \) and solve for \( y \). - **x-intercepts:** Set \( y = 0 \) and solve the quadratic equation for \( x \). When graphing, remember: - The graph is a parabola opening downwards because the coefficient of \( x^2 \) is negative. - Plot the vertex and intercepts accurately to depict the parabola’s shape.
Transcribed Image Text:**Graphing Quadratic Functions** Graph the quadratic function \( y = -x^2 + 2x + 3 \). Analyze its key characteristics, including the vertex and the intercepts. ### Key Elements to Identify: 1. **Vertex:** - Use the vertex formula \( x = -\frac{b}{2a} \) to find the x-coordinate. - Calculate \( y \) by substituting \( x \) back into the equation. 2. **Intercepts:** - **y-intercept:** Set \( x = 0 \) and solve for \( y \). - **x-intercepts:** Set \( y = 0 \) and solve the quadratic equation for \( x \). When graphing, remember: - The graph is a parabola opening downwards because the coefficient of \( x^2 \) is negative. - Plot the vertex and intercepts accurately to depict the parabola’s shape.
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